I don't know if you have all of the graphics bells and whistles boxes checked i.e. 32 rather than 16 etc but the more memory you have, the better. Maybe buy more memory ... up to 2 gigs ... memory is relatively cheap nowdays and easy to install.
With the ATI card I don't think you would have any problem installing and running SH1 using the Don Wells method:
http://www.subsowespac.org/sh_xp/silent_hunterxp.shtml
Again, with DosBox the more memory the better. The games are a little sluggish under DosBox.
http://www.subsowespac.org/sh_tech.shtml
Art Anker